2,735 research outputs found
Numerical Integration of Nonlinear Wave Equations for General Relativity
A second-order numerical implementation is given for recently derived
nonlinear wave equations for general relativity. The Gowdy T cosmology is
used as a test bed for studying the accuracy and convergence of simulations of
one-dimensional nonlinear waves. The complete freedom in space-time slicing in
the present formulation is exploited to compute in the Gowdy line-element.
Second-order convergence is found by direct comparison of the results with
either analytical solutions for polarized waves, or solutions obtained from
Gowdy's reduced wave equations for the more general unpolarized waves. Some
directions for extensions are discussed.Comment: 19 pages (LaTex), 3 figures (ps
Past and future gauge in numerical relativity
Numerical relativity describes a discrete initial value problem for general
relativity. A choice of gauge involves slicing space-time into space-like
hypersurfaces. This introduces past and future gauge relative to the
hypersurface of present time. Here, we propose solving the discretized Einstein
equations with a choice of gauge in the future and a dynamical gauge in the
past. The method is illustrated on a polarized Gowdy wave.Comment: To appear in Class Quantum Grav, Let
Electric Charge and Magnetic Flux on Rotating Black Holes in a Force-Free Magnetosphere
The electric charge on rotating black holes is calculated to be ~ BJ in the
force-free configuration of Ghosh (2000), with a horizon flux of ~ BM^2. This
charge is gravitationally weak for B ~ 10^{15} G, so that the Kerr metric
applies. Being similar to the electric charge of a magnetar, both electric
charge and magnetic flux should be, in sign and order of magnitude, continuous
during stellar collapse into a black hole. Extraction of the rotational energy
from newly formed black holes may proceed by interaction with the magnetic
field. Keywords:black hole physics --magnetic fieldsComment: 11 pages, no figure, restructured with sections and revisions in
abstarct and in the text, version accepted for MNRA
Gravitational wave frequencies and energies in hypernovae
A torus develops a state of suspended accretion against a magnetic wall
around a rapidly rotating black hole formed in core-collapse hypernovae. It
hereby emits about 10% of the black hole spin-energy in gravitational radiation
from a finite number of multipole mass moments. We quantify the relation
between the frequency of quadrupole gravitational radiation and the energy
output in torus winds by , where denotes the mass of the black
hole. We propose that irradiates the remnant stellar envelope from
within. We identify with energies erg inferred from X-ray
observations on matter injecta; and the poloidal curvature in the magnetic wall
with the horizon opening angle in baryon poor outflows that power true GRB
energies of erg.Comment: To appear in AP
Uniqueness in MHD in divergence form: right nullvectors and well-posedness
Magnetohydrodynamics in divergence form describes a hyperbolic system of
covariant and constraint-free equations. It comprises a linear combination of
an algebraic constraint and Faraday's equations. Here, we study the problem of
well-posedness, and identify a preferred linear combination in this divergence
formulation. The limit of weak magnetic fields shows the slow magnetosonic and
Alfven waves to bifurcate from the contact discontinuity (entropy waves), while
the fast magnetosonic wave is a regular perturbation of the hydrodynamical
sound speed. These results are further reported as a starting point for
characteristic based shock capturing schemes for simulations with
ultra-relativistic shocks in magnetized relativistic fluids.Comment: To appear in J Math Phy
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